Fine structure and centrifugal distortion in the electronic and microwave spectra of O2 and SO

The fine structure theory of ³Σ states in diatomic molecules is re-examined with particular emphasis on centrifugal distortion in the triplet splitting parameters. The theoretical results are compared with optical and microwave data for the ³Σ ground states of O₂ and SO. Excellent agreement is found between theoretical predictions and experimental results concerning the centrifugal distortion in the spin-spin splitting for both O₂ and SO. However, in contrast to ab initio calculations this agreement indicates that the second-order contribution to the spin-spin splitting is of minor importance. The theoretical value of the centrifugal distortion in the spin-rotation coupling constant is about twice the experimental one for O₂. It is pointed out that a slight transition towards coupling case (c) yields a reasonable explanation for this discrepancy.     

A reduced form of the spin-spin centrifugal distortion Hamiltonian for orthorhombic asymmetric top molecules

The spin-spin centrifugal distortion Hamiltonian for an asymmetric top molecule in a given vibrational level of an open-shell electronic state with S ? 1 may contain more parameters than can be determined from the observed energy levels. This paper describes the reduction of the Hamiltonian by means of a unitary transformation to a form suitable for fitting to observed energies. It is established that there are six determinable spin-spin centrifugal distortion parameters for a molecule of orthorhombic symmetry; the corresponding matrix elements are derived for both Hund’s case (a) and case (b) coupling schemes.     

Theoretical study of the spin-orbit coupling in the X2Π state of OH

The spin-orbit coupling constant, A(r), as a function of internuclear distance (r) was computed for the X²Π state of OH, using the microscopic spin-orbit Hamiltonian, extended basis sets, and extensive configuration-interaction wavefunctions. Our best theoretical results are in excellent agreement with the “experimental” A(r) functions deduced from an inversion of the observed A_v. Our calculated first-order contributions to A_v, v ≤ 10, obtained by vibrationally averaging our theoretical A(r) function using the X²Π RKR potential, differ from experiment by less than 0.12%. A minimum occurs in the A_v at v = 7 in agreement with experiment, reflecting the local minimum in A(r) near 2.8 bohr. The second-order contributions to A_v are only about 0.1% for v ≤ 10. They arise mainly from the A²Σ⁺ state for the lower vibrational levels, but each of the A²Σ⁺, B²Σ⁺, (1)²Σ^?, (1)⁴Σ^?, and (1)²Δ states contributes significantly for higher vibrational levels. Spin-orbit centrifugal distortion parameters, A_Dv and a_Dv, are reported for v ≤ 6. The theoretical A_Dv are also in excellent agreement with experiment when the “experimental” A(r) function has the same slope at the equilibrium separation as that obtained from the effective spin-rotation constants of OH, OD, and OT.     

Centrifugal distortion analysis of the rotational spectrum of aziridine: Comparison of different Hamiltonians

Previous measurements of rotational spectrum of aziridine up to 1.85 THz have been supplemented by new data in 225-660 GHz frequency range. A total of 1465 transitions (915 of them are newly assigned ones) with maximum values of J = 59 and K_c = 50 were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although aziridine is an asymmetric oblate top, the combination (A, III^r) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination (S, III^r). It is explained that the failure of the combination (A, III^r) is due to the large value of the parameter σ=(2C-A-B)/(A-B) which makes some sextic centrifugal distortion constants much too large impeding the convergence of the Hamiltonian. It is also shown that the calculation of the centrifugal distortion constants from a force field is sometimes an ill-conditioned operation. Finally, the use of a non-reduced Hamiltonian (with six quartic centrifugal distortion constants) was successful in the particular case thanks to the method of predicate observations.     

High-resolution infrared and theoretical study of the fundamental bands ν6, ν7, ν9 and ν13 of 1,2,3-thiadiazole

The Fourier transform gas-phase IR spectrum of 1,2,3-thiadiazole, C₂H₂N₂S, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the 700-1100 cm⁻¹ spectral region. Four fundamental bands ν₆(A^/; 1101.8 cm⁻¹), ν₇(A^/; 1038.8 cm⁻¹), ν₉(A^/, 858.9 cm⁻¹), and ν₁₃(A^//; 746.2 cm⁻¹) have been analyzed using the Watson model in A-reduction. Two additional bands, ν₈ (A^/; 894.6 cm⁻¹) and ν₁₂(A^//; 881.2 cm⁻¹) were assigned by their weak Q-branches. Ground state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from fits. A number of weak global and local interactions are present in the bands. The resonances identified were qualitatively explained by Coriolis type perturbations with neighboring levels. Ground state rotational and quartic centrifugal distortion constants, anharmonic frequencies, and vibration-rotational α-constants predicted by quantum chemical calculations using a cc-pVTZ basis and B3LYP methodology, have been compared with the present experimental data, where there is generally good agreement.     

The lower excited states of CS: A study of extensive spin-orbit perturbations

We present previously unpublished data on the A¹Π, e³Σ^?, d³Δ_i, $\text{a′}{}^3\text{Σ}{}^{\mathrm{+}}$, and a³Π states of CS from uv emission and absorption transitions to the X¹Σ⁺ ground state. Term values obtained from d³Δ_i ← a³Π ir emission bands are also included. Rotational analyses are presented for about 50 new fine-structure components in some 30 new vibrational levels, together with extended data and analyses for many of the previously observed levels. The data now availabe for these five electronic states more than triples that previously published. Vibrational numbering for the e, d, and a′ states is established by data for minor isotopes. In a Hund's case a-b basis, off-diagonal spin-orbit elements (incipient case c effects) produce extensive coupling among these levels, not only for perturbation crossings but also between levels widely separated in energy. A systematic deperturbation requires two stages, which are iterated. Term values computed from the spectral lines are used to fit parameters of Hamiltonian matrices for groups of nearby, coupled levels. Additional shifts are computed by second-order perturbation theory from the electronic interactions deduced from vibronic coupling elements. The resultant parameters satisfy certain tests for self-consistency; they conform to low-order polynomials in $\text{v +}\text{1}\text{2}$, and vibrational overlap factors from wave-functions computed with RKR potential curves are proportional to the vibronic coupling elements, to within experimental error in most cases. To obtain this self-consistency, we have computed and applied normally neglected centrifugal distortion effects in the off-diagonal coupling elements and in the second-order perturbation sums. We also present and interpret the diagonal spin-orbit fine structure in the a and d states, including the centrifugal distortion parameters, A_D, for the latter, and values for several fitted second-order elements. Possible assignments for three additional perturbations of the A¹Π state and one faint band are discussed in view of ¹Δ, ¹Σ^?, and ⁵Π states that are also expected to occur in the region studied. Tentative parameters for the D¹Δ state are obtained from one possible set of assignments.     

Diode laser spectrum and analysis of the 882-cm−1 band of s-tetrazine

A high-resolution diode laser spectrum of the 882-cm^?1 band of s-tetrazine has been obtained. A complete rotational analysis of this band, incorporating quartic and sextic centrifugal distortion coefficients, has been carried out. The rotational constants A, B, and C have been determined with an accuracy better than 10^?5 cm^?1. The analysis has shown the band to be A-type and, on this basis, the vibrational assignment of this band has been revised from ν₁₂ to ν₁₄.     

Simultaneous analysis of the microwave and infrared spectra of 14ND3 and 15ND3 for the ν2 excited state

The data on the inversion spectrum in the ν₂ state of ¹⁴ND₃ [F. Scappini, A. Guarnieri, and G. DiLonardo, J. Mol. Spectrosc.95, 20–29 (1982)] have been extended by measuring frequencies of 25 new transitions. A simultaneous least-squares analysis of these data with the ground state microwave transition frequencies and the diode laser measurements of the ν₂ band has been carried out. Improved sets of molecular parameters have been obtained for ¹⁴ND₃ and ¹⁵ND₃, including the ground and ν₂ state inversion splittings, ν₂ band origins, rotational and centrifugal distortion constants, and the parameters of the Δk = ±3n vibrational-rotational interactions.     

The uv spectrum of 18OD

The combined high-resolution ultraviolet (uv) absorption spectrum of ¹⁶OD and ¹⁸OD was obtained. State selective measurements of the transitions from the electronic ground state to the first excited electronic state, $\text{A}\text{?}{}^2\text{Σ}{}^{\mathrm{+}}\text{←}\text{X}\text{?}{}^2\text{Π}$, in the 0-0 vibronic band were performed by means of a narrow bandwidth dye laser system. Evaluation of these transition frequencies in wave-numbers yielded molecular constants as well as rotational term values for each of the isotopic species. A computer program based on a linearized least-squares procedure was used to determine the molecular constants and term values. The term value formulas which were employed for this purpose, take into account the Λ splitting and the centrifugal distortion of the diatomic species. The transitions, recalculated from the semiempirically determined term values agree with the measured absorption lines to better than 0.1 cm^?1. The following molecular constants are reported: B, D, H, the rotational constants of the ²Π and ²Σ⁺ states; O₀, P₀, Q₀, the constants of the Λ splitting of the ²Π state; A and A₁; the constants of the spin-orbit coupling of the ²Π state; and γ₀, the constant of the p doubling of the ²Σ⁺ state. Futhermore, term values up to J″ and J′ of 25.5 and the corresponding uv transitions are given.     

The general harmonic force field of fluoroform

Anharmonicity constants and harmonic frequencies of HC¹²F₃ and DC¹²F₃ are obtained for the first time. These data are combined with ζ^z, ζ^x,y and centrifugal distortion constants and carbon-13 frequency shifts to obtain, using the display method, the general harmonic force field (GHFF) of fluoroform. All 12 force constants in the GHFF, including off-diagonal elements in the A₁ block, are determined with significance. The carbon-13 frequency shifts proved to be most important for precise determination of A₁ off-diagonal elements. The GHFF is compared with the predictions of the Hybrid Orbital Force Field (HOFF).     

Internal rotation in methyl silane by avoided-crossing molecular-beam spectroscopy

The avoided-crossing molecular-beam electric-resonance technique was applied to methyl silane in the ground torsional state. A new type of anticrossing is introduced which breaks the torsional symmetry and obeys the selection rules ΔJ = 0, K = +1 /a3 ?1. For these “barrier” anticrossings, the values of the crossing fields E_c yield directly the internal rotation splittings; the E_c are independent of the difference (A-B) in the rotational constants. Such anticrossings were observed for J from 1 to 6. Studies were also conducted of several “rotational” anticrossings (J, K) = (1, ±1) /a3 (2, 0) for which E_c does depend on (A-B). The normal rotational transition (J, K) = (1, 0) ← (0, 0) was observed in the ground torsional state using the molecular beam spectrometer. The present data on CH₃²⁸SiH₃ were combined with Hirota's microwave spectra and analyzed with the torsion-rotation Hamiltonian including all quartic centrifugal distortion terms. In addition to evaluating B and several distortion constants, determinations were made of the moment of inertia of the methyl top I_α = 3.165(5) amu-Ų, the effective rotational constant A^eff = 56 189.449(32) MHz, and the effective height of the threefold barrier to internal rotation V₃^eff = 592.3359(73) cm^?1. The correlations leading to these two effective constants are discussed and the true values of A and V₃ are determined within certain approximations. For the isotopic species CH₃³⁰SiH₃, barrier and rotational anticrossings were observed. The isotopic changes in A and V₃ were determined, as well as an upper limit to the corresponding change in I_α.     

The rotational a-type sepctra of 15N-labeled diazirine,H2CN2

The rotational a-type spectra of isotopically enriched diazirine isotopomers, H₂¹²C¹⁴N¹⁵N and H₂¹²C¹⁵N₂, have been recorded in the region between 8 and 300 GHZ; the latter isotopomer has been observed for the first time. Using Watson's A-reduced Hamiltonian, the rotational constants and the quartic and some sextic centrifugal distortion constants have been determined for the ground vibrational states.     

The high-resolution infrared spectrum of pyrrole between 900 and 1500 cm revisited

The Fourier transform gas-phase infrared spectrum of pyrrole, C₄H₅N, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the 900-1500 cm⁻¹ spectral region. Four fundamental bands, ν₈(A₁; 1016.9 cm⁻¹), ν₂₃(B₂; 1049.1 cm⁻¹), ν₇(A₁; 1074.6 cm⁻¹), ν₂₀(B₂; 1424.4 cm⁻¹) and the overtone band 2ν₁₆(A₁; 962.7 cm⁻¹) have been analysed using the Watson model. The ν₈ and 2ν₁₆ bands are unperturbed; the ν₇ and ν₂₃ bands are locally perturbed, while the ν₂₀ band is globally perturbed by weak c-Coriolis resonance. Upper state vibrational term values, and rotational and centrifugal distortion constants, have been obtained from fits using S-reduction and I^r-representation as well as A-reduction and III^r-representation. A set of ground state rotational and centrifugal distortion constants using A-reduction was obtained from a simultaneous fit of ground state combination differences from all five bands and previous microwave and millimetre-wave data.     

Diborane: High-resolution infrared rovibration studies of 10B2D6

Studies of five comparatively unperturbed infrared active bands in the spectrum of ¹⁰B₂D₆ were undertaken with a resolution of ca. 0.05 cm^?1. These comprise three type-A bands (ν₁₇, ν₁₈, and ν₅ + ν₁₅), one type-B band (ν₈), and one type-C band (ν₁₄). Ground-state rotational and quartic centrifugal distortion constants were determined for the first time from a total of over 400 combination differences. Sets of upper-state parameters were determined for all five bands studied, and the effects of a number of minor Coriolis interactions between fundamental vibrations are discussed.     

Calculation of the magnetic hyperfine structure in the ground electronic state of HCCO

In this paper we analyze the spin-spin hyperfine interaction in the two components of the ground electronic state of the free π radical HCCO, A²A′[²Π] and X²A″. Electronic mean values of the Fermi contact constants of all magnetic nuclei [¹H, ¹³C₁, ¹³C₂,¹⁷O] are calculated using models that include the electron-correlation correction, primarily CCSD method in the cc-pwCVTZ basis set and B3LYP functional in the cc-pCVQZ basis set. Also, we have calculated components of the anisotropic hyperfine tensor for the ground X²A″ state. The dependence of hyperfine coupling constants (HFCCs) on the two bending coordinates is examined, and the results of HCC bending (vibrational) averaging of electronic mean values are presented for both states. It is demonstrated that electronic and subsequent vibrational averaging of the HFCCs suffices for obtaining results that are in good agreement with available experimental findings (for proton) in the X²A″ state, owing to a small geometry dependence of these quantities, and relatively distant minimum from linearity.     

Rotational Spectrum of the Excited Vibrational States of DCOOH and Assignment of Optically Pumped Laser Transitions

The rotational spectrum of DCOOH in the 175–335 GHz region was investigated. Analysis of the spectrum made it possible to assign several dozen transitions in the ν₆, ν₈, and ν₅vibrational states and to determine the rotational and centrifugal distortion constants. The derived parameters of the ν₆state allowed four optically pumped laser transitions to be assigned. In addition, the ground state parameters for DCOOH and D¹³COOH have been improved and for the first time those for DC¹⁸OOH and DCO¹⁸OH have been obtained.     

Centrifugal Distortion Constants and Potential Energy Curves of the InBr Molecule

Using: semiclassical calculation the centrifugal distortion constants have been obtained for the X¹ σ⁺, A³II₀ and B³II₁ electronic states of InBr.

Reliable RKR potential energy curves have been constructed.     

LiC分子基态及其低电子激发态的多参考组态相互作用方法研究

采用包含Davidson修正的多参考组态相互作用(MRCI+Q)方法结合6-311++G(3df,3pd)基组计算了LiC分子基态(X4Σ-)以及五个低电子激发态(a2Π,b2Δ,c2Σ-,d2Σ+,A4Π)的势能曲线.将得到的势能曲线拟合到Murrell-Sorbie解析势能函数形式,确定了对应态的平衡结构Re、谐振频率ωe和离解能De等光谱数据,计算值与仅有的几个其他结果进行了比较.通过求解核运动的薛定谔方程首次报道了LiC分子几个低电子态在J=0下的振动能级、转动惯量和六个离心畸变常数(Dν,Hν,Lν,Mν,Nν和Oν).     

Centrifugal distortion constants and force field of HClCO

Measurement of the a- and b-type rotational transitions of formyl chloride, HClCO, was extended up to J = 50 and k_a = 5 ← 4 in the frequency range of 8 to 200 GHz. Accurate rotational parameters including the sextic centrifugal distortion constants were determined from the observed spectrum for the ³⁵Cl and ³⁷Cl species. The τ defect in the planarity relations of the quartic centrifugal distortion constants was found to be negligibly small. From the quartic centrifugal distortion constants and the previously reported fundamental vibrational frequencies, force constants of formyl chloride were calculated by assuming the Urey-Bradley force field.     

The high-resolution infrared spectrum of thiophene between 600 and 1200 cm: A spectroscopic and theoretical study of the fundamental bands ν6, ν7, ν13, and the c-Coriolis interacting dyad ν5, ν19

The Fourier transform infrared spectrum of gaseous thiophene, C₄H₄S, has been recorded in the 600-1200 cm⁻¹ spectral region with a resolution of ca. 0.0030 cm⁻¹. Five fundamental bands ν₁₃ (B₁, 712.1 cm⁻¹), ν₇ (A₁; 840.0 cm⁻¹), ν₆ (A₁; 1036.4 cm⁻¹), ν₅ (A₁; 1081.5 cm⁻¹) and ν₁₉ (B₂; 1084.0 cm⁻¹) have been analysed by the standard Watson model (A-reduction). Ground state rotational and quartic centrifugal distortion constants have been obtained from a simultaneous fit of ground state combination differences from four of these bands and previous microwave transitions. Upper state spectroscopic constants have been obtained for all five bands from single band fits using the Watson model. A strong c-Coriolis resonance perturbs the close lying ν₅ and ν₁₉ bands. We have analysed this dyad system by a model including first and second order Coriolis resonance using the theoretically predicted Coriolis coupling constant . From this analysis we locate the previously unobserved ν₁₉ band at 1083.969 cm⁻¹. The rotational constants, ground state quartic centrifugal distortion constants, anharmonic frequencies, and vibration-rotational constants (α-constants) predicted by quantum chemical calculations using a cc-pVTZ basis with B3LYP methodology, are compared with the present experimental data, where there is generally good agreement. A complete set of anharmonic frequencies and α-constants for all fundamental levels of the molecule is given.